Physics World Model — Modality Catalog
37 imaging modalities with descriptions, experimental setups, and reconstruction guidance.
Arterial Spin Labeling (ASL) MRI
Arterial Spin Labeling (ASL) MRI
Brachytherapy Imaging
Brachytherapy Imaging
CEST MRI
CEST MRI
Cone-Beam Computed Tomography
Cone-beam CT (CBCT) uses a divergent cone-shaped X-ray beam and a flat-panel 2D detector to acquire volumetric data in a single rotation, unlike fan-beam CT which acquires slice-by-slice. The 3D Feldkamp-Davis-Kress (FDK) algorithm performs approximate filtered back-projection for cone geometry. CBCT is widely used in dental, ENT, and image-guided radiation therapy. Primary artifacts include cone-beam artifacts at large cone angles, scatter, and truncation. Sparse-view CBCT reduces scan time and dose but introduces streak artifacts.
Cone-Beam Computed Tomography
Description
Cone-beam CT (CBCT) uses a divergent cone-shaped X-ray beam and a flat-panel 2D detector to acquire volumetric data in a single rotation, unlike fan-beam CT which acquires slice-by-slice. The 3D Feldkamp-Davis-Kress (FDK) algorithm performs approximate filtered back-projection for cone geometry. CBCT is widely used in dental, ENT, and image-guided radiation therapy. Primary artifacts include cone-beam artifacts at large cone angles, scatter, and truncation. Sparse-view CBCT reduces scan time and dose but introduces streak artifacts.
Principle
Cone-Beam CT uses a divergent cone-shaped X-ray beam and a 2-D flat-panel detector to acquire a volumetric CT dataset in a single rotation. Unlike multi-slice CT with a narrow fan beam, CBCT covers the full volume simultaneously, enabling faster acquisition but with increased scatter and cone-beam artifacts compared to conventional CT.
How to Build the System
Mount a flat-panel detector (typically 30×40 cm, CsI scintillator) opposite an X-ray tube on a rotating gantry or C-arm. Common implementations: dental CBCT (small FOV, 90 kVp), image-guided radiation therapy CBCT (kV source on linac gantry), and C-arm CBCT (interventional). Calibrate: geometric parameters (source-detector distances, isocenter), detector offset corrections, and scatter correction LUTs.
Common Reconstruction Algorithms
- FDK (Feldkamp-Davis-Kress) cone-beam filtered back-projection
- Iterative CBCT (SART, SIRT with cone-beam projector)
- Scatter correction (measurement-based or Monte Carlo simulation)
- Motion-compensated CBCT (4D-CBCT for respiratory motion)
- Deep-learning CBCT-to-CT synthesis for radiation therapy planning
Common Mistakes
- Severe scatter artifacts (cupping, shading) in large FOV acquisitions
- Cone-beam artifacts near the edges of the FOV (Feldkamp approximation breaks down)
- Truncation artifacts when anatomy extends outside the FOV
- Motion artifacts in thorax/abdomen from respiratory and cardiac motion
- Insufficient angular sampling causing streak artifacts
How to Avoid Mistakes
- Apply scatter correction (anti-scatter grid, software correction, or beam-blocker method)
- Limit cone angle or use exact reconstruction algorithms for large cone angles
- Use extended FOV techniques (shifted detector, multiple scans) for large anatomy
- Apply 4D-CBCT or gated acquisition for moving anatomy
- Acquire sufficient projections (≥600 for a full rotation) with uniform angular spacing
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred (64,64) image, but cone-beam CT acquires a sinogram of shape (n_angles, n_detector_rows * n_detector_cols) from a 2D detector rotating around the patient — the data is a set of cone-beam projections, not a blurred image
- CBCT cone-beam geometry introduces axial cone-angle artifacts (Feldkamp approximation errors) that are absent from the widefield model — any reconstruction expecting cone-beam projection data will fail with the blurred image
How to Correct the Mismatch
- Use the CBCT operator implementing cone-beam projection (Radon transform in 3D divergent geometry) for each source-detector angle, producing the correct sinogram/projection data shape
- Reconstruct using FDK (Feldkamp-Davis-Kress) algorithm or iterative cone-beam methods (SART, ADMM) with the correct cone-beam system matrix
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Feldkamp et al., 'Practical cone-beam algorithm', JOSA A 1, 612-619 (1984)
Canonical Datasets
- ICASSP 2024 CBCT Challenge
Confocal Laser Endomicroscopy (CLE)
Confocal Laser Endomicroscopy (CLE)
Contrast-Enhanced Ultrasound (CEUS)
Contrast-Enhanced Ultrasound (CEUS)
Diffuse Optical Tomography
Diffuse optical tomography (DOT) reconstructs 3D maps of tissue optical properties (absorption mu_a and reduced scattering mu_s') by measuring near-infrared light transport through highly scattering tissue. Multiple source-detector pairs on the tissue surface sample the diffuse photon field. The forward model is the diffusion equation: light propagation is modelled as a diffusive process with the photon fluence depending on the spatial distribution of mu_a and mu_s'. Reconstruction linearizes around a homogeneous background (Born/Rytov approximation) or uses nonlinear iterative methods. Applications include breast imaging and functional brain imaging (fNIRS-DOT).
Diffuse Optical Tomography
Description
Diffuse optical tomography (DOT) reconstructs 3D maps of tissue optical properties (absorption mu_a and reduced scattering mu_s') by measuring near-infrared light transport through highly scattering tissue. Multiple source-detector pairs on the tissue surface sample the diffuse photon field. The forward model is the diffusion equation: light propagation is modelled as a diffusive process with the photon fluence depending on the spatial distribution of mu_a and mu_s'. Reconstruction linearizes around a homogeneous background (Born/Rytov approximation) or uses nonlinear iterative methods. Applications include breast imaging and functional brain imaging (fNIRS-DOT).
Principle
Diffuse Optical Tomography reconstructs 3-D maps of tissue optical properties (absorption μₐ and reduced scattering μ'ₛ) from measurements of multiply scattered near-infrared light transmitted through tissue. Multiple source-detector pairs on the tissue surface provide overlapping sensitivity profiles. The diffusion equation models light propagation in the multiple-scattering regime.
How to Build the System
Place fiber-coupled NIR sources (670-850 nm laser diodes, CW or frequency-domain modulated at 100-300 MHz, or time-domain pulsed) and detector fibers (avalanche photodiodes or PMTs) on the tissue surface in an array. A multiplexer switches between source positions. For breast DOT, 32-128 optode positions on a cup or ring geometry. Calibrate with known optical phantoms (Intralipid + ink solutions).
Common Reconstruction Algorithms
- Normalized Born approximation (linearized diffuse optical tomography)
- Nonlinear Newton-type iterative reconstruction (Gauss-Newton, Levenberg-Marquardt)
- Finite-element method (FEM) based forward solver + Tikhonov regularization
- TOAST++ (Time-resolved Optical Absorption and Scattering Tomography)
- Deep-learning DOT (learned regularization, direct inversion networks)
Common Mistakes
- Poor optode-tissue coupling due to hair, uneven surfaces, or insufficient pressure
- Inadequate source-detector pair coverage causing reconstruction blind spots
- Cross-talk between source channels if multiplexing is not properly timed
- Using the diffusion approximation too close to sources or in low-scattering regions
- Ignoring tissue heterogeneity in the background optical property estimate
How to Avoid Mistakes
- Use spring-loaded optodes with coupling checks; shave hair in the measurement area
- Design source-detector geometry with overlapping sensitivity to cover the volume of interest
- Ensure clean channel switching with adequate settling time between multiplexed measurements
- Use higher-order transport models (radiative transfer) near sources if needed
- Initialize reconstruction with patient-specific anatomical prior (from MRI or CT)
Forward-Model Mismatch Cases
- The widefield fallback produces a 2D (64,64) image, but Diffuse Optical Tomography acquires boundary measurements (source-detector pairs) — output shape (64,) is a 1D vector of photon counts at detector positions
- DOT measurement physics involves diffuse light propagation through scattering tissue (modeled by the diffusion equation), which is fundamentally different from surface-level Gaussian blur — the fallback cannot model subsurface absorption and scattering
How to Correct the Mismatch
- Use the DOT operator that models photon transport via the diffusion equation: Jacobian maps from interior optical properties (absorption, scattering) to boundary measurements at each source-detector pair
- Reconstruct interior absorption/scattering maps using Tikhonov-regularized inversion or iterative methods (conjugate gradient) with the correct diffusion-equation-based forward model
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Arridge, 'Optical tomography in medical imaging', Inverse Problems 15, R41-R93 (1999)
- Boas et al., 'Imaging the body with diffuse optical tomography', IEEE Signal Processing Magazine 18, 57-75 (2001)
Canonical Datasets
- UCL DOT phantom datasets
- BU fNIRS-DOT brain imaging benchmarks
Diffusion MRI (DTI)
Diffusion MRI measures the random Brownian motion of water molecules in tissue by applying magnetic field gradient pulses that encode microscopic displacement. The signal attenuation follows S = S_0 * exp(-b * D_eff) where b is the diffusion weighting factor and D_eff is the effective diffusion coefficient along the gradient direction. Acquiring measurements in multiple gradient directions enables estimation of the diffusion tensor (DTI) and derived scalar maps (FA, MD, AD, RD). Advanced models (NODDI, CSD) resolve intra-voxel fiber crossings. Primary degradations include EPI distortion, eddy currents, and motion sensitivity.
Diffusion MRI (DTI)
Description
Diffusion MRI measures the random Brownian motion of water molecules in tissue by applying magnetic field gradient pulses that encode microscopic displacement. The signal attenuation follows S = S_0 * exp(-b * D_eff) where b is the diffusion weighting factor and D_eff is the effective diffusion coefficient along the gradient direction. Acquiring measurements in multiple gradient directions enables estimation of the diffusion tensor (DTI) and derived scalar maps (FA, MD, AD, RD). Advanced models (NODDI, CSD) resolve intra-voxel fiber crossings. Primary degradations include EPI distortion, eddy currents, and motion sensitivity.
Principle
Diffusion MRI sensitizes the MR signal to the Brownian motion of water molecules by applying strong magnetic field gradient pulses (Stejskal-Tanner scheme). In fibrous tissue (e.g., white matter), water diffuses preferentially along fibers, creating directional diffusion anisotropy. Diffusion Tensor Imaging (DTI) models this as a 3×3 tensor; higher-order models (HARDI, CSD) resolve crossing fibers.
How to Build the System
Acquire on a 3T scanner with high-performance gradients (80 mT/m, 200 T/m/s). Use spin-echo EPI with multiple b-values (e.g., b=0, 1000, 2000 s/mm²) and 30-300 diffusion directions uniformly distributed on the sphere. Include reverse-phase-encode b=0 images for EPI distortion correction. Multi-band (SMS) acceleration reduces scan time. Typical parameters: 2 mm isotropic, TE 60-90 ms, TR 3-5 s.
Common Reconstruction Algorithms
- DTI tensor fitting (least-squares or weighted least-squares)
- CSD (Constrained Spherical Deconvolution) for fiber orientation distribution
- NODDI (Neurite Orientation Dispersion and Density Imaging)
- Probabilistic tractography (FSL probtrackx, MRtrix3 iFOD2)
- Deep-learning tract segmentation (TractSeg, DeepBundle)
Common Mistakes
- Eddy current and EPI geometric distortions not corrected, causing tract errors
- Insufficient number of diffusion directions for the chosen model complexity
- Using DTI in regions with crossing fibers, producing incorrect FA and tract directions
- Susceptibility-induced signal dropout near air-tissue interfaces (sinuses, temporal lobes)
- Head motion between diffusion volumes causing inter-volume misalignment
How to Avoid Mistakes
- Apply FSL eddy or equivalent for eddy current, motion, and susceptibility correction
- Use ≥30 directions for DTI, ≥60 for CSD, and ≥90 for multi-shell models
- Use multi-fiber models (CSD, NODDI) in regions known to have crossing fibers
- Use reduced FOV or multi-shot EPI near susceptibility-prone regions
- Include interspersed b=0 volumes for robust motion and drift correction
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred spatial image, but diffusion MRI applies magnetic field gradients to encode Brownian water motion — the Stejskal-Tanner signal attenuation S = S_0*exp(-b*D) is not modeled
- Diffusion MRI acquires multiple volumes at different b-values and gradient directions to measure the diffusion tensor at each voxel — the widefield single-image model cannot encode directional water diffusivity or fiber orientation
How to Correct the Mismatch
- Use the diffusion MRI operator that applies Stejskal-Tanner encoding: y_i = FFT(x * exp(-b_i * g_i^T * D * g_i)) for each gradient direction g_i and b-value b_i
- Reconstruct diffusion tensors (DTI) or fiber orientation distributions (CSD, NODDI) from the multi-direction, multi-b-value measurements using the correct diffusion-weighted forward model
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Basser et al., 'MR diffusion tensor spectroscopy and imaging', Biophysical Journal 66, 259-267 (1994)
- Sotiropoulos et al., 'Advances in diffusion MRI acquisition and processing in the HCP', NeuroImage 80, 125-143 (2013)
Canonical Datasets
- Human Connectome Project (HCP) diffusion data
- UK Biobank diffusion imaging
Digital Breast Tomosynthesis (DBT)
Digital Breast Tomosynthesis (DBT)
Doppler Ultrasound
Doppler ultrasound measures blood flow velocity by detecting the frequency shift of ultrasound echoes reflected from moving red blood cells. The Doppler shift f_d = 2*f_0*v*cos(theta)/c relates velocity v to the observed frequency shift. Color Doppler maps 2D velocity fields by applying autocorrelation estimators to ensembles of pulse-echo data at each spatial location. A wall filter (high-pass) separates slow tissue clutter from blood flow signals. Challenges include aliasing when velocity exceeds the Nyquist limit (PRF/2) and angle-dependence of the velocity estimate.
Doppler Ultrasound
Description
Doppler ultrasound measures blood flow velocity by detecting the frequency shift of ultrasound echoes reflected from moving red blood cells. The Doppler shift f_d = 2*f_0*v*cos(theta)/c relates velocity v to the observed frequency shift. Color Doppler maps 2D velocity fields by applying autocorrelation estimators to ensembles of pulse-echo data at each spatial location. A wall filter (high-pass) separates slow tissue clutter from blood flow signals. Challenges include aliasing when velocity exceeds the Nyquist limit (PRF/2) and angle-dependence of the velocity estimate.
Principle
Doppler ultrasound measures blood flow velocity by detecting the frequency shift of echoes reflected from moving red blood cells. The Doppler equation relates the frequency shift to velocity: Δf = 2f₀·v·cos(θ)/c, where θ is the beam-flow angle. Color Doppler maps velocity spatially, spectral Doppler provides velocity-time waveforms at a sample volume, and power Doppler shows flow amplitude regardless of direction.
How to Build the System
Use a clinical ultrasound system with Doppler capability. For vascular studies, use a linear array transducer (5-12 MHz). Steer the beam to achieve a Doppler angle <60° to the vessel axis. Set the velocity scale (PRF) to match expected flow speeds (avoid aliasing). For spectral Doppler, place the sample volume within the vessel lumen and adjust the gate size. Angle correction must be applied for accurate velocity measurements.
Common Reconstruction Algorithms
- Autocorrelation-based color flow estimation (Kasai algorithm)
- FFT spectral analysis for pulsed-wave Doppler
- Clutter filtering (wall filtering) to remove tissue motion
- Power Doppler (amplitude mode) for slow flow detection
- Ultrafast Doppler (plane-wave compounding) for functional ultrasound
Common Mistakes
- Doppler angle >60° causing large velocity measurement errors
- Aliasing in color or spectral Doppler from PRF set too low for flow velocity
- Wall filter too aggressive, eliminating slow venous flow signals
- Blooming artifact in color Doppler from excessive gain
- Not correcting for angle in spectral Doppler velocity measurements
How to Avoid Mistakes
- Maintain Doppler angle <60°; ideally 30-60° for best accuracy
- Increase PRF (velocity scale) until aliasing resolves; or use CW Doppler
- Reduce wall filter setting when looking for slow flow (venous, microvascular)
- Reduce color Doppler gain until color just fills the vessel without overflow
- Always apply angle correction cursor parallel to the vessel wall for spectral Doppler
Forward-Model Mismatch Cases
- The widefield fallback produces a 2D (64,64) image, but Doppler ultrasound acquires velocity-encoded data — output includes blood flow velocity maps estimated from phase shifts between consecutive pulses
- Doppler measurement relies on the frequency shift of backscattered ultrasound from moving blood cells (f_d = 2*v*cos(theta)*f_0/c) — the widefield spatial blur has no velocity or frequency-shift information
How to Correct the Mismatch
- Use the Doppler ultrasound operator that models pulsed-wave Doppler: multiple pulses along each line, with phase differences between returns encoding blood flow velocity
- Estimate velocity using autocorrelation (Kasai estimator) or spectral Doppler analysis on the correctly modeled multi-pulse RF data, then map to color flow images
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Kasai et al., 'Real-time two-dimensional blood flow imaging using an autocorrelation technique', IEEE Trans. Sonics Ultrasonics 32, 458-464 (1985)
Canonical Datasets
- Clinical Doppler benchmark collections
Dual-Energy X-ray Absorptiometry
DEXA measures bone mineral density (BMD) by acquiring two X-ray projections at different energies (typically 70 and 140 kVp) and decomposing the attenuation into bone and soft-tissue components using their known energy-dependent mass attenuation coefficients. The dual-energy forward model is y_E = I_0(E) * exp(-(mu_b(E)*t_b + mu_s(E)*t_s)) + n for each energy E. Output is areal BMD (g/cm2) and T-score for osteoporosis diagnosis. Precision errors of ~1% are achievable.
Dual-Energy X-ray Absorptiometry
Description
DEXA measures bone mineral density (BMD) by acquiring two X-ray projections at different energies (typically 70 and 140 kVp) and decomposing the attenuation into bone and soft-tissue components using their known energy-dependent mass attenuation coefficients. The dual-energy forward model is y_E = I_0(E) * exp(-(mu_b(E)*t_b + mu_s(E)*t_s)) + n for each energy E. Output is areal BMD (g/cm2) and T-score for osteoporosis diagnosis. Precision errors of ~1% are achievable.
Principle
Dual-Energy X-ray Absorptiometry uses two X-ray beam energies to decompose the body into bone mineral and soft tissue compartments. The differential attenuation of the two energies allows separation of bone from soft tissue. Bone mineral density (BMD, g/cm²) is computed by comparing attenuation to calibration phantoms.
How to Build the System
A DEXA scanner (Hologic Discovery/Horizon or GE Lunar) uses a fan-beam or pencil-beam X-ray source with two energies (typically 70 and 140 kVp, or k-edge filtration). The detector is directly opposite the source below the patient table. Daily quality assurance with a calibration phantom (anthropomorphic spine) is mandatory. Cross-calibration is needed when changing scanners. Scan modes include AP spine, dual femur, whole body, and lateral vertebral assessment.
Common Reconstruction Algorithms
- Dual-energy decomposition (two-material model: bone + soft tissue)
- Edge detection for region-of-interest (ROI) identification
- BMD calculation relative to calibration phantom
- T-score / Z-score computation against normative databases
- Body composition analysis (lean mass, fat mass from whole-body scans)
Common Mistakes
- Patient positioning errors (rotation, wrong vertebral level) affecting BMD
- Not removing metal objects (belts, jewelry) that artifactually increase BMD
- Comparing BMD values from different scanner manufacturers without cross-calibration
- Degenerative changes (osteophytes) falsely elevating spine BMD
- Analyzing the wrong vertebral levels or including fractured vertebrae
How to Avoid Mistakes
- Standardize patient positioning with positioning aids; verify on scout image
- Remove all metal from scan field; use lateral spine view to avoid artifacts
- Use same scanner for serial monitoring; cross-calibrate if changing equipment
- Evaluate AP spine image for degenerative changes; consider lateral spine or femur
- Follow ISCD guidelines for vertebral inclusion/exclusion criteria in analysis
Forward-Model Mismatch Cases
- The widefield fallback produces a single 2D (64,64) image, but DEXA acquires dual-energy X-ray measurements — output shape (2,64,64) has two channels (high and low energy) for material decomposition
- DEXA uses the energy-dependent difference in attenuation between bone and soft tissue to measure bone mineral density — the single-energy widefield blur cannot distinguish materials and produces no BMD information
How to Correct the Mismatch
- Use the DEXA operator that models dual-energy Beer-Lambert transmission: y_E = I_0(E) * exp(-(mu_bone(E)*t_bone + mu_tissue(E)*t_tissue)) for E = low and high energy
- Decompose the dual-energy measurements into bone and soft tissue components using the known energy-dependent attenuation coefficients to compute areal bone mineral density (g/cm^2)
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Blake & Fogelman, 'The role of DXA bone density scans in the diagnosis and treatment of osteoporosis', Postgrad. Med. J. 83, 509-517 (2007)
Canonical Datasets
- NHANES DXA reference data (CDC)
Fluoroscopy
Fluoroscopy provides real-time continuous X-ray imaging for guiding interventional procedures. The forward model is the same Beer-Lambert projection as radiography but at much lower dose per frame (typically 1 uGy/frame at 15-30 fps) resulting in severely photon-limited images. Temporal redundancy from the video stream enables frame-to-frame denoising and recursive filtering. Primary challenges include low SNR, motion blur from patient/organ movement, and veiling glare from scatter.
Fluoroscopy
Description
Fluoroscopy provides real-time continuous X-ray imaging for guiding interventional procedures. The forward model is the same Beer-Lambert projection as radiography but at much lower dose per frame (typically 1 uGy/frame at 15-30 fps) resulting in severely photon-limited images. Temporal redundancy from the video stream enables frame-to-frame denoising and recursive filtering. Primary challenges include low SNR, motion blur from patient/organ movement, and veiling glare from scatter.
Principle
Fluoroscopy provides real-time continuous X-ray imaging for guiding interventional procedures. A pulsed or continuous X-ray beam produces live projection images at 7.5-30 fps on a flat-panel detector. The trade-off is between frame rate, radiation dose, and image quality. Temporal filtering and dose-saving modes reduce patient exposure while maintaining diagnostic quality.
How to Build the System
A C-arm fluoroscopy unit has an X-ray tube and flat-panel detector on a C-shaped gantry that can rotate around the patient. Modern systems use pulsed fluoroscopy (variable pulse rate 3.75-30 fps) with automatic brightness control. Install last-image-hold and virtual collimation features. Calibrate geometric distortion for 3-D cone-beam reconstruction capability. Regular dosimetry checks (DAP meter calibration) are mandatory.
Common Reconstruction Algorithms
- Recursive temporal averaging (IIR filtering for noise reduction)
- Contrast-enhanced subtraction (road-mapping for angiography)
- Motion-compensated temporal filtering
- Cone-beam CT reconstruction from rotational fluoroscopy runs
- Deep-learning frame interpolation for reduced pulse-rate operation
Common Mistakes
- Excessive radiation dose from unnecessarily high frame rate or continuous mode
- Image lag / ghosting from slow detector response at low dose
- Geometric distortion from C-arm flex not calibrated
- Scatter degrading contrast in lateral or oblique views of thick anatomy
- Patient skin dose exceeding threshold (2 Gy) during long procedures
How to Avoid Mistakes
- Use lowest acceptable pulse rate; employ last-image-hold instead of continuous fluoro
- Use fast flat-panel detectors (GOS or CsI with fast readout) to minimize lag
- Perform regular geometric calibration with a phantom for accurate 3D reconstruction
- Collimate tightly and use appropriate anti-scatter grids
- Monitor cumulative dose (DAP) and skin dose during procedures; rotate beam angles
Forward-Model Mismatch Cases
- The widefield fallback applies additive Gaussian blur, but fluoroscopy follows X-ray Beer-Lambert attenuation with real-time temporal dynamics — the exponential transmission model and dynamic contrast are absent
- Fluoroscopy operates at much lower dose rates than radiography, requiring modeling of quantum mottle (Poisson noise at very low photon counts) and image intensifier/flat-panel detector gain — the widefield noise model is wrong
How to Correct the Mismatch
- Use the fluoroscopy operator implementing real-time X-ray transmission: y = I_0 * exp(-A*x) with Poisson quantum noise, modeling the low-dose regime and detector response
- Apply temporal filtering (recursive averaging) or deep-learning denoising tuned for the correct Poisson noise level of fluoroscopic sequences
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Defined by IEC 62220-1 standard for fluoroscopy detector characterization
Canonical Datasets
- Clinical fluoroscopy sequences (institution-specific)
Functional MRI (BOLD)
Functional MRI detects neural activity indirectly via the blood-oxygen-level dependent (BOLD) contrast mechanism. Active brain regions increase local blood flow and oxygenation, altering the ratio of diamagnetic oxyhemoglobin to paramagnetic deoxyhemoglobin, causing T2* signal changes of 1-5%. Data is acquired with fast gradient-echo EPI sequences at high temporal resolution (TR 0.5-2s). The forward model includes the hemodynamic response function (HRF) convolved with neural activity. Primary challenges include physiological noise, head motion, and the low CNR of the BOLD signal.
Functional MRI (BOLD)
Description
Functional MRI detects neural activity indirectly via the blood-oxygen-level dependent (BOLD) contrast mechanism. Active brain regions increase local blood flow and oxygenation, altering the ratio of diamagnetic oxyhemoglobin to paramagnetic deoxyhemoglobin, causing T2* signal changes of 1-5%. Data is acquired with fast gradient-echo EPI sequences at high temporal resolution (TR 0.5-2s). The forward model includes the hemodynamic response function (HRF) convolved with neural activity. Primary challenges include physiological noise, head motion, and the low CNR of the BOLD signal.
Principle
Functional MRI detects brain activity indirectly through the Blood Oxygen Level Dependent (BOLD) contrast mechanism. Neural activity increases local blood flow and oxygenation, changing the ratio of diamagnetic oxyhemoglobin to paramagnetic deoxyhemoglobin. This alters the local T2* relaxation time, producing a small (~1-5 %) signal change detectable by gradient-echo EPI sequences acquired rapidly at whole-brain coverage.
How to Build the System
Use a 3T MRI scanner with a 32-64 channel head coil. Acquire multi-band (simultaneous multi-slice) gradient-echo EPI sequences (TR 0.5-1.5 s, TE ~30 ms, 2 mm isotropic voxels, multiband factor 4-8). Include a high-resolution T1w structural scan for registration. Physiological monitoring (pulse oximetry, respiratory bellows) enables noise regression. Use foam padding to minimize head motion.
Common Reconstruction Algorithms
- General Linear Model (GLM) for task-based fMRI (FSL FEAT, SPM)
- ICA (Independent Component Analysis) for resting-state networks
- Seed-based functional connectivity analysis
- Motion correction and nuisance regression (6-parameter rigid body + CompCor)
- Deep-learning denoising and parcellation (BrainNetCNN, fMRIPrep pipeline)
Common Mistakes
- Excessive head motion causing false activations or connectivity artifacts
- Not correcting for physiological noise (cardiac, respiratory) in the signal
- Insufficient statistical correction for multiple comparisons (inflated false positives)
- Using too long a TR, missing the hemodynamic response in fast event-related designs
- Geometric distortion in EPI not corrected before registration to structural scan
How to Avoid Mistakes
- Use prospective motion correction and strict motion exclusion criteria (<0.5 mm FD)
- Acquire and regress physiological signals; use ICA-based denoising (ICA-AROMA)
- Apply proper multiple-comparison correction (FWE, FDR, cluster-based thresholding)
- Use multiband EPI for sub-second TR to adequately sample the HRF
- Acquire field maps (B₀) and apply distortion correction (topup, fieldmap-based)
Forward-Model Mismatch Cases
- The widefield fallback applies spatial Gaussian blur, but fMRI measures the BOLD (Blood Oxygen Level Dependent) signal via T2*-weighted MRI — the hemodynamic response function (HRF) convolution with neural activity is completely absent
- fMRI acquisition occurs in k-space (Fourier domain) with EPI readout, and the signal of interest is a tiny (~1-5%) temporal modulation — the widefield spatial blur cannot model the temporal hemodynamic dynamics or k-space encoding
How to Correct the Mismatch
- Use the fMRI operator that models BOLD signal generation: y(t) = FFT_acquisition(x_baseline * (1 + delta_BOLD(t))), where delta_BOLD = HRF * neural_activity encodes brain activation
- Analyze using GLM (general linear model) with the hemodynamic response function, or ICA/connectivity analysis, applied to correctly modeled time-series MRI data
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Ogawa et al., 'Brain magnetic resonance imaging with contrast dependent on blood oxygenation', PNAS 87, 9868-9872 (1990)
- Glasser et al., 'The minimal preprocessing pipelines for the Human Connectome Project', NeuroImage 80, 105-124 (2013)
Canonical Datasets
- Human Connectome Project (HCP) 3T (1200 subjects)
- UK Biobank brain imaging
Functional Near-Infrared Spectroscopy (fNIRS)
Functional Near-Infrared Spectroscopy (fNIRS)
Industrial CT
Industrial CT
Intravascular Ultrasound (IVUS)
Intravascular Ultrasound (IVUS)
Magnetic Resonance Imaging
MRI forms images by exciting hydrogen nuclei with RF pulses in a strong magnetic field (1.5-7T) and measuring the emitted RF signal with receive coils. Spatial encoding uses gradient fields to map signal frequency and phase to spatial position, acquiring data in k-space (spatial frequency domain). The forward model for parallel imaging is y_c = F_u * S_c * x + n_c where F_u is the undersampled Fourier transform, S_c are coil sensitivity maps, and n_c is complex Gaussian noise. Accelerated MRI undersamples k-space (4-8x) and uses SENSE, GRAPPA, or deep-learning (E2E-VarNet) for reconstruction.
Magnetic Resonance Imaging
Description
MRI forms images by exciting hydrogen nuclei with RF pulses in a strong magnetic field (1.5-7T) and measuring the emitted RF signal with receive coils. Spatial encoding uses gradient fields to map signal frequency and phase to spatial position, acquiring data in k-space (spatial frequency domain). The forward model for parallel imaging is y_c = F_u * S_c * x + n_c where F_u is the undersampled Fourier transform, S_c are coil sensitivity maps, and n_c is complex Gaussian noise. Accelerated MRI undersamples k-space (4-8x) and uses SENSE, GRAPPA, or deep-learning (E2E-VarNet) for reconstruction.
Principle
Magnetic Resonance Imaging measures the precession of hydrogen nuclear spins in a strong magnetic field (1.5-7 T). Radiofrequency pulses tip spins away from equilibrium, and gradient fields spatially encode the MR signal into k-space (spatial frequency domain). The image is obtained by inverse Fourier transform of k-space data. Contrast depends on tissue T1, T2, and proton density via the pulse sequence timing parameters.
How to Build the System
A clinical MRI scanner has a superconducting magnet (1.5 T or 3 T), gradient coils (40-80 mT/m, 200 T/m/s slew rate), RF transmit body coil, and local receive coil arrays (8-128 channels). The patient lies inside the bore on a table. Key calibrations: center frequency, RF transmit calibration (B₁ mapping), shimming (B₀ homogeneity), and gradient eddy current compensation. Use pulse sequences optimized for the clinical question (T1w, T2w, FLAIR, DWI, etc.).
Common Reconstruction Algorithms
- Inverse FFT (standard Cartesian k-space reconstruction)
- GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisitions)
- SENSE (SENSitivity Encoding) parallel imaging
- Compressed sensing MRI (L1-wavelet + TV regularization)
- Deep-learning MRI reconstruction (fastMRI, variational networks, E2E-VarNet)
Common Mistakes
- Aliasing artifacts from insufficient FOV or acceleration too aggressive
- Motion artifacts (ghosting in phase-encode direction) from patient or physiological motion
- B₀ inhomogeneity causing geometric distortion and signal dropout (especially at 3T+)
- Fat-water chemical shift artifacts at fat-tissue interfaces
- Incorrect coil sensitivity maps causing SENSE/GRAPPA reconstruction artifacts
How to Avoid Mistakes
- Set FOV to cover the anatomy with margin; use saturation bands to suppress aliasing
- Apply motion correction (navigator, PROPELLER, prospective correction) for moving anatomy
- Perform careful shimming; use distortion correction maps for EPI sequences
- Use fat suppression or water-fat separation (Dixon) sequences
- Acquire adequate auto-calibration data for parallel imaging; use robust coil maps
Forward-Model Mismatch Cases
- The widefield fallback produces real-valued spatially blurred output, but MRI acquires complex-valued k-space data via the Fourier transform with undersampling mask — all phase information is lost with the fallback
- The fallback applies spatial-domain convolution, but MRI measurement occurs in Fourier domain (k-space): y = M * F * x — using the fallback means compressed-sensing MRI reconstruction (L1-wavelet, E2E-VarNet) cannot function
How to Correct the Mismatch
- Use the MRI operator that applies the 2D Fourier transform followed by an undersampling mask: y = M * FFT2(x), producing complex-valued k-space measurements
- Reconstruct using parallel imaging (GRAPPA, SENSE) or compressed sensing (L1-wavelet + TV regularization) that operate on the Fourier-domain measurements with known sampling pattern
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Pruessmann et al., 'SENSE: Sensitivity encoding for fast MRI', Magnetic Resonance in Medicine 42, 952-962 (1999)
- Zbontar et al., 'fastMRI: An open dataset and benchmarks for accelerated MRI', arXiv:1811.08839 (2018)
- Sriram et al., 'End-to-End Variational Networks for Accelerated MRI Reconstruction (E2E-VarNet)', MICCAI 2020
Canonical Datasets
- fastMRI (knee: 1594 volumes, brain: 6970 volumes)
- Calgary-Campinas (brain, multi-coil)
- SKM-TEA (Stanford knee MRI)
Mammography
Full-field digital mammography (FFDM) produces high-resolution X-ray projection images of compressed breast tissue for cancer screening. The low-energy X-ray beam (25-32 kVp with W/Rh or Mo/Mo target-filter) maximizes soft tissue contrast. Amorphous selenium flat-panel detectors provide direct conversion with ~50 um pixel pitch. The forward model follows Beer-Lambert with energy-dependent attenuation. Primary challenges include overlapping tissue structures, microcalcification detection, and dense breast tissue masking lesions.
Mammography
Description
Full-field digital mammography (FFDM) produces high-resolution X-ray projection images of compressed breast tissue for cancer screening. The low-energy X-ray beam (25-32 kVp with W/Rh or Mo/Mo target-filter) maximizes soft tissue contrast. Amorphous selenium flat-panel detectors provide direct conversion with ~50 um pixel pitch. The forward model follows Beer-Lambert with energy-dependent attenuation. Primary challenges include overlapping tissue structures, microcalcification detection, and dense breast tissue masking lesions.
Principle
Mammography uses low-energy X-rays (25-35 kVp) with specialized anode/filter combinations (Mo/Mo, Mo/Rh, W/Rh) to optimize contrast between breast tissue types (adipose, glandular, calcifications). Breast compression reduces thickness and scatter, improving contrast and reducing dose. Digital mammography uses flat-panel detectors for direct or indirect X-ray detection.
How to Build the System
A dedicated mammography unit with a compression paddle, specialized X-ray tube (Mo, Rh, or W anode), and high-resolution flat-panel detector (50-100 μm pixel size, amorphous selenium for direct conversion). Automatic optimization of target/filter and kVp based on compressed breast thickness. Regular quality assurance per ACR/MQSA requirements: phantom images, SNR measurements, artifact checks, and AEC calibration.
Common Reconstruction Algorithms
- Contrast-limited adaptive histogram equalization (CLAHE) for display
- Computer-aided detection (CAD) for microcalcification and mass detection
- Digital breast tomosynthesis (DBT) reconstruction (FBP or iterative)
- Deep-learning breast density classification (BI-RADS categories)
- Synthetic 2D mammography from DBT volumes
Common Mistakes
- Insufficient breast compression, increasing dose and reducing contrast
- Positioning errors cutting off breast tissue (especially axillary tail)
- Grid artifacts or grid cutoff from misaligned Bucky grid
- Exposure errors from AEC sensor placed over dense tissue vs. adipose
- Motion blur from long exposure times in thick or dense breasts
How to Avoid Mistakes
- Apply firm, consistent compression; verify thickness readout is reasonable
- Follow standardized positioning protocols (CC, MLO) with technologist training
- Verify grid alignment and use reciprocating grid to eliminate grid lines
- Position AEC sensor appropriately for breast density; adjust manually if needed
- Use shortest possible exposure with adequate mAs; consider large-angle tomosynthesis
Forward-Model Mismatch Cases
- The widefield fallback applies Gaussian blur, but mammography uses low-energy X-ray transmission (25-35 kVp) with tissue-specific attenuation coefficients optimized for fat/glandular tissue contrast — the physics model is fundamentally different
- Mammographic image formation involves compression geometry, scatter grid rejection, anti-scatter grid, and detector-specific MTF — none of these are captured by a simple spatial Gaussian blur
How to Correct the Mismatch
- Use the mammography operator implementing Beer-Lambert transmission at mammographic energies with tissue-specific attenuation: y = I_0 * exp(-mu_tissue * t) for fat, glandular, and calcification components
- Include scatter rejection model, detector quantum efficiency (DQE), and geometric magnification for accurate forward modeling and quantitative breast density estimation
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- VinDr-Mammo, Scientific Data 2023
- Lee et al., 'A curated mammography dataset (CBIS-DDSM)', Scientific Data 4, 170177 (2017)
Canonical Datasets
- VinDr-Mammo (5000 4-view exams)
- CBIS-DDSM (curated DDSM subset)
- INbreast (410 images, Moreira et al.)
MR Angiography (MRA)
MR Angiography (MRA)
MR Elastography (MRE)
MR Elastography (MRE)
MR Fingerprinting (MRF)
MR Fingerprinting (MRF)
MR Spectroscopy
Magnetic resonance spectroscopy (MRS) measures the concentration of metabolites in a localized tissue volume by exploiting the chemical shift — the slight difference in Larmor frequency caused by the electronic environment of different molecular groups. The free induction decay (FID) or spin echo signal is Fourier-transformed to a spectrum where each metabolite produces characteristic peaks (e.g. NAA at 2.01 ppm, Cr at 3.03 ppm). Quantification involves fitting the spectrum to a linear combination of basis spectra (LCModel, OSPREY). Challenges include low SNR, spectral overlap, water/lipid suppression, and B0 inhomogeneity causing linewidth broadening.
MR Spectroscopy
Description
Magnetic resonance spectroscopy (MRS) measures the concentration of metabolites in a localized tissue volume by exploiting the chemical shift — the slight difference in Larmor frequency caused by the electronic environment of different molecular groups. The free induction decay (FID) or spin echo signal is Fourier-transformed to a spectrum where each metabolite produces characteristic peaks (e.g. NAA at 2.01 ppm, Cr at 3.03 ppm). Quantification involves fitting the spectrum to a linear combination of basis spectra (LCModel, OSPREY). Challenges include low SNR, spectral overlap, water/lipid suppression, and B0 inhomogeneity causing linewidth broadening.
Principle
MR Spectroscopy measures the chemical shift spectrum of nuclear spins (usually ¹H) from a localized volume in the body, providing concentrations of metabolites such as NAA, creatine, choline, lactate, myo-inositol, and glutamate/glutamine. Chemical shift differences (in ppm) arise from the varying electronic shielding of nuclei in different molecular environments.
How to Build the System
Use PRESS or STEAM single-voxel localization on a 1.5T or 3T scanner. Voxel sizes are typically 2×2×2 cm³ for brain. Suppress the dominant water signal (CHESS or VAPOR water suppression). Acquire 64-256 averages (NEX) for adequate SNR. Shimming is critical: water linewidth should be <12 Hz (3T) for the voxel. Multi-voxel CSI (Chemical Shift Imaging) maps metabolite distributions but requires longer acquisition and careful lipid suppression.
Common Reconstruction Algorithms
- LCModel (frequency-domain linear combination fitting)
- TARQUIN (open-source time-domain fitting)
- jMRUI (time-domain quantification with AMARES/QUEST)
- HSVD (Hankel SVD) for water removal and baseline correction
- Deep-learning spectral quantification (DeepSpectra, convolutional fitting)
Common Mistakes
- Poor shimming producing broad linewidths that overlap metabolite peaks
- Voxel placed partly outside the brain, contaminating spectrum with lipid signal
- Insufficient water suppression saturating the spectrum baseline
- Too few averages, producing noisy spectra with unreliable metabolite estimates
- Ignoring macromolecular baseline contributions in fitting
How to Avoid Mistakes
- Iteratively shim the voxel to achieve <12 Hz water linewidth (3T) before acquisition
- Place the voxel with margin from skull and subcutaneous fat; use outer-volume suppression
- Optimize water suppression parameters; acquire separate water reference for quantification
- Acquire sufficient averages: 128-256 for metabolites at low concentration (e.g., GABA)
- Include macromolecular basis set or measured baseline in the fitting model
Forward-Model Mismatch Cases
- The widefield fallback produces a spatial image, but MR Spectroscopy acquires frequency-domain spectra encoding chemical composition — metabolite peaks (NAA, choline, creatine, lactate) at specific ppm values are entirely absent
- MRS data is a 1D free induction decay (FID) or spectrum per voxel, not a 2D spatial image — the widefield blur destroys the spectral dimension that encodes metabolite concentrations
How to Correct the Mismatch
- Use the MRS operator that models the free induction decay: y(t) = sum_k(a_k * exp(i*2pi*f_k*t) * exp(-t/T2_k)) for each metabolite k, then FFT to produce the frequency spectrum
- Quantify metabolite concentrations by fitting the spectrum (LCModel, TARQUIN) or using deep-learning spectral quantification with the correctly modeled spectral forward model
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Provencher, 'Estimation of metabolite concentrations from localized in vivo proton NMR spectra (LCModel)', MRM 30, 672-679 (1993)
- Wilson et al., 'Methodological consensus on clinical proton MRS of the brain (MRSinMRS)', NMR in Biomedicine 34, e4484 (2021)
Canonical Datasets
- ISMRM MRS fitting challenge datasets
- Big GABA multi-site MRS data
PET/CT
PET/CT
PET/MR
PET/MR
Photoacoustic Imaging
Photoacoustic imaging (PAI) is a hybrid modality that combines optical absorption contrast with ultrasonic detection. Short laser pulses (nanoseconds) are absorbed by tissue chromophores (hemoglobin, melanin), causing thermoelastic expansion that generates broadband ultrasound waves detected by transducer arrays. The forward model involves the photoacoustic wave equation: the initial pressure p_0(r) is proportional to the absorbed optical energy. Reconstruction inverts the acoustic propagation using delay-and-sum (DAS) or model-based algorithms.
Photoacoustic Imaging
Description
Photoacoustic imaging (PAI) is a hybrid modality that combines optical absorption contrast with ultrasonic detection. Short laser pulses (nanoseconds) are absorbed by tissue chromophores (hemoglobin, melanin), causing thermoelastic expansion that generates broadband ultrasound waves detected by transducer arrays. The forward model involves the photoacoustic wave equation: the initial pressure p_0(r) is proportional to the absorbed optical energy. Reconstruction inverts the acoustic propagation using delay-and-sum (DAS) or model-based algorithms.
Principle
Photoacoustic imaging converts absorbed pulsed laser light into ultrasound via thermoelastic expansion. Short laser pulses (<10 ns) are absorbed by tissue chromophores (hemoglobin, melanin), causing rapid thermal expansion that generates broadband acoustic waves. These waves are detected by ultrasound transducers and reconstructed to form images reflecting optical absorption contrast at ultrasonic spatial resolution.
How to Build the System
Combine a tunable pulsed laser (Nd:YAG pumped OPO, 680-1100 nm, 5-20 ns pulses, 10-20 Hz) with an ultrasound transducer array (linear or curved, 5-40 MHz). Deliver light via fiber bundle to the tissue surface adjacent to the transducer. Use a multi-channel DAQ (12-14 bit, 40-100 MS/s) to record acoustic signals. For tomographic PAT, surround the sample with a ring or spherical array of transducers.
Common Reconstruction Algorithms
- Universal back-projection for photoacoustic tomography
- Time-reversal reconstruction
- Model-based iterative reconstruction with acoustic heterogeneity
- Spectral unmixing for multi-wavelength functional PA imaging
- Deep-learning PA image reconstruction (U-Net, pixel-wise inversion)
Common Mistakes
- Insufficient laser fluence reaching target depth due to tissue scattering
- Acoustic heterogeneity (speed-of-sound variations) causing image distortion
- Limited-view artifacts from incomplete transducer coverage around the sample
- Coupling medium mismatch between transducer and tissue
- Laser safety violations from excessive skin surface fluence (>20 mJ/cm²)
How to Avoid Mistakes
- Use NIR wavelengths (700-900 nm optical window) for deeper penetration
- Use speed-of-sound correction maps or joint reconstruction for heterogeneous media
- Maximize angular coverage of transducer array; use virtual-detector techniques
- Use appropriate acoustic coupling gel or water bath between transducer and tissue
- Monitor laser fluence at the tissue surface; comply with ANSI Z136.1 MPE limits
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred (64,64) image, but photoacoustic imaging acquires time-resolved pressure signals at transducer elements — output shape (n_time, n_detectors) represents acoustic wave arrivals, not an image
- Photoacoustic signal generation involves optical absorption → thermoelastic expansion → acoustic wave propagation — the widefield blur has no connection to the optical-acoustic conversion physics
How to Correct the Mismatch
- Use the photoacoustic operator that models the forward problem: laser absorption creates initial pressure p_0(r) = Gamma * mu_a * Phi(r), then acoustic waves propagate to transducer elements
- Reconstruct using time-reversal, back-projection, or model-based iterative methods that invert the acoustic wave equation from measured pressure time series to initial pressure distribution
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Wang & Yao, 'Photoacoustic microscopy and computed tomography', Nature Methods 13, 627-638 (2016)
- Manwar et al., 'OADAT: Optoacoustic dataset', J. Biophotonics 2024
Canonical Datasets
- OADAT (optoacoustic benchmark)
- IPASC consensus datasets
Portal Imaging (EPID)
Portal Imaging (EPID)
Positron Emission Tomography
PET images the 3D distribution of a positron-emitting radiotracer (e.g. 18F-FDG) by detecting coincident 511 keV annihilation photon pairs along lines of response (LORs). The forward model is a system matrix encoding the detection probability for each voxel-LOR pair, incorporating attenuation, scatter, randoms, and detector response. Reconstruction uses iterative ML-EM/OSEM algorithms with attenuation correction from co-registered CT. Low count rates yield Poisson noise; time-of-flight (TOF) information improves SNR.
Positron Emission Tomography
Description
PET images the 3D distribution of a positron-emitting radiotracer (e.g. 18F-FDG) by detecting coincident 511 keV annihilation photon pairs along lines of response (LORs). The forward model is a system matrix encoding the detection probability for each voxel-LOR pair, incorporating attenuation, scatter, randoms, and detector response. Reconstruction uses iterative ML-EM/OSEM algorithms with attenuation correction from co-registered CT. Low count rates yield Poisson noise; time-of-flight (TOF) information improves SNR.
Principle
Positron Emission Tomography detects pairs of 511 keV gamma rays emitted in opposite directions when a positron from a radiotracer annihilates with an electron. Coincidence detection of the two photons defines a line of response (LOR). Many LORs from different angles are reconstructed into a 3-D activity distribution map, providing functional and metabolic information.
How to Build the System
A PET scanner consists of a ring of scintillation detector blocks (LYSO or LSO crystals coupled to SiPMs) surrounding the patient. Each detector block has a matrix of small crystals (3-4 mm pitch). Coincidence electronics pair detected events within a timing window (4-6 ns for TOF-PET). Modern digital PET systems achieve 200-300 ps timing resolution for time-of-flight. Daily quality checks include detector normalization, timing calibration, and sensitivity phantom scans.
Common Reconstruction Algorithms
- OSEM (Ordered Subset Expectation Maximization)
- 3D OSEM with resolution modeling (PSF reconstruction)
- TOF-OSEM (time-of-flight enhanced OSEM)
- Attenuation correction from CT (PET/CT) or Dixon MR (PET/MR)
- Deep-learning PET denoising (low-count to full-count prediction)
Common Mistakes
- Incorrect attenuation correction map (misregistration between PET and CT)
- Patient motion between PET and CT causing attenuation-emission mismatch
- Metal artifacts in CT propagating into PET attenuation correction
- Scatter correction errors in patients with large body habitus
- SUV calculation errors from incorrect weight, dose, or timing entries
How to Avoid Mistakes
- Verify PET-CT registration quality; use respiratory gating for thorax/abdomen
- Minimize time between CT and PET acquisitions; co-register if needed
- Use MAR-corrected CT or MR-based attenuation correction to avoid metal artifacts
- Use Monte Carlo scatter correction models validated for the patient population
- Double-check injected dose, patient weight, injection time, and decay correction
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred (64,64) image, but PET acquires sinogram data of shape (n_angles, n_radial) from coincidence detection of annihilation photon pairs — output shape (32,64) vs (64,64)
- PET measurement physics (positron emission → annihilation → 511 keV photon pair → coincidence detection) is fundamentally different from optical blur — the fallback cannot model attenuation correction, scatter, randoms, or detector normalization
How to Correct the Mismatch
- Use the PET operator that models the system matrix: y = A*x + scatter + randoms, where A encodes line-of-response geometry and attenuation
- Reconstruct using OSEM (Ordered Subsets Expectation Maximization) with the correct system matrix, attenuation map, and scatter/randoms estimates
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Shepp & Vardi, 'Maximum likelihood reconstruction for emission tomography', IEEE TMI 1, 113-122 (1982)
- Gatidis et al., 'AutoPET Challenge 2022', MICCAI 2022
Canonical Datasets
- AutoPET Challenge (whole-body FDG-PET/CT)
- TCIA PET/CT collections
Proton Therapy Imaging
Proton Therapy Imaging
Shear-Wave Elastography
Shear-wave elastography (SWE) quantifies tissue stiffness by generating shear waves using an acoustic radiation force impulse (ARFI) push and tracking their propagation with ultrafast ultrasound imaging (10,000+ fps). The shear wave speed c_s is related to the shear modulus by mu = rho * c_s^2, enabling quantitative mapping of Young's modulus E = 3*mu (assuming incompressibility). The technique is clinically validated for liver fibrosis staging (F0-F4) and breast lesion characterization. Challenges include shear wave attenuation in deep tissue and reflections from boundaries.
Shear-Wave Elastography
Description
Shear-wave elastography (SWE) quantifies tissue stiffness by generating shear waves using an acoustic radiation force impulse (ARFI) push and tracking their propagation with ultrafast ultrasound imaging (10,000+ fps). The shear wave speed c_s is related to the shear modulus by mu = rho * c_s^2, enabling quantitative mapping of Young's modulus E = 3*mu (assuming incompressibility). The technique is clinically validated for liver fibrosis staging (F0-F4) and breast lesion characterization. Challenges include shear wave attenuation in deep tissue and reflections from boundaries.
Principle
Shear-wave elastography measures tissue stiffness by tracking the propagation speed of shear waves generated by an acoustic radiation force impulse (ARFI) or external vibration. Shear-wave speed is proportional to the square root of the shear modulus: cₛ = √(μ/ρ). Stiffer tissues (fibrosis, tumors) have faster shear-wave propagation. Results are displayed as quantitative elasticity maps (in kPa or m/s).
How to Build the System
Use a clinical ultrasound system with shear-wave elastography mode (Supersonic Imagine Aixplorer, Siemens ARFI/VTQ, or GE 2D-SWE). The transducer generates a focused push pulse to create shear waves, then tracks their propagation with ultrafast plane-wave imaging (up to 10,000 fps). Place the ROI in a region free of large vessels and interfaces. Patient should hold breath for liver measurements. Calibrate with an elasticity phantom.
Common Reconstruction Algorithms
- Time-to-peak shear-wave arrival estimation
- Phase-gradient shear-wave speed inversion
- 2-D shear-wave elastography mapping (real-time SWE)
- Transient elastography (FibroScan 1-D measurement)
- Deep-learning elasticity estimation from B-mode + SWE data
Common Mistakes
- Pre-compression by pressing transducer too hard, artifactually increasing stiffness
- Measuring in the near-field where push pulse is unreliable
- Not having patient hold breath for liver measurements (respiratory motion invalidates SWE)
- Placing ROI near large vessels or liver capsule causing boundary artifacts
- Not waiting for the measurement to stabilize (IQR/median >30 % indicates unreliable data)
How to Avoid Mistakes
- Apply light transducer pressure with coupling gel; avoid compressing tissue
- Place measurement ROI at 1.5-2 cm depth in liver; avoid the near-field zone
- Instruct patient to suspend breathing calmly during each SWE measurement
- Avoid ROI placement near vessels, liver edges, or ribs
- Acquire ≥10 valid measurements and check IQR/median <30 % per EFSUMB guidelines
Forward-Model Mismatch Cases
- The widefield fallback produces a 2D (64,64) image, but elastography measures tissue displacement/strain from mechanical wave propagation — output includes displacement maps at multiple time points
- Elastography estimates tissue stiffness (Young's modulus) from shear wave speed, which requires tracking mechanical wave propagation through tissue — the widefield Gaussian blur has no connection to mechanical wave physics
How to Correct the Mismatch
- Use the elastography operator that models mechanical excitation (acoustic radiation force or external vibration) and tracks the resulting tissue displacement using ultrasound or MRI phase encoding
- Estimate shear wave speed from displacement propagation, then compute tissue stiffness: E = 3*rho*c_s^2, using the correct wave propagation and displacement tracking forward model
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Bercoff et al., 'Supersonic shear imaging: a new technique for soft tissue elasticity mapping', IEEE TUFFC 51, 396-409 (2004)
- Barr et al., 'Elastography assessment of liver fibrosis', Radiology 276, 845-861 (2015)
Canonical Datasets
- Clinical SWE liver fibrosis benchmark data
Single Photon Emission Computed Tomography
SPECT images the 3D distribution of a gamma-emitting radiotracer (e.g. 99mTc-sestamibi) by detecting single photons with rotating gamma cameras equipped with parallel-hole collimators. The collimator creates a projection of the activity distribution, and multiple angles enable tomographic reconstruction. The forward model includes collimator response (depth-dependent blurring), photon attenuation, and scatter. Reconstruction uses OSEM with corrections for attenuation (AC), scatter (SC), and resolution recovery (RR).
Single Photon Emission Computed Tomography
Description
SPECT images the 3D distribution of a gamma-emitting radiotracer (e.g. 99mTc-sestamibi) by detecting single photons with rotating gamma cameras equipped with parallel-hole collimators. The collimator creates a projection of the activity distribution, and multiple angles enable tomographic reconstruction. The forward model includes collimator response (depth-dependent blurring), photon attenuation, and scatter. Reconstruction uses OSEM with corrections for attenuation (AC), scatter (SC), and resolution recovery (RR).
Principle
Single Photon Emission Computed Tomography detects single gamma-ray photons emitted by a radiotracer (⁹⁹ᵐTc, ¹²³I, ²⁰¹Tl) using a rotating gamma camera with a parallel-hole or pinhole collimator. The collimator provides directional sensitivity at the cost of low geometric efficiency (~0.01 %). Projections from multiple angles are reconstructed into 3-D activity maps.
How to Build the System
A dual-head gamma camera (e.g., Siemens Symbia, GE Discovery) with NaI(Tl) scintillator crystals (9.5 mm thick) and parallel-hole collimators rotates around the patient (typically 60-128 angular stops over 360°). For cardiac SPECT, use dedicated CZT-based cameras with pinhole or multi-pinhole collimators. Acquire in step-and-shoot or continuous rotation mode. Energy windows are set around the photopeak (e.g., 140 keV ± 10 % for ⁹⁹ᵐTc).
Common Reconstruction Algorithms
- FBP with ramp-Butterworth filter
- OSEM with attenuation and scatter correction
- Resolution recovery (collimator-detector response modeling in OSEM)
- CT-based attenuation correction (SPECT/CT)
- Deep-learning SPECT reconstruction (dose reduction, resolution enhancement)
Common Mistakes
- Insufficient count statistics causing noisy, unreliable reconstructions
- Not correcting for depth-dependent collimator blur (resolution degrades with distance)
- Attenuation artifacts in uncorrected SPECT (false defects in myocardial perfusion)
- Patient motion during the long SPECT acquisition (15-30 minutes)
- Incorrect energy window or scatter window setup leading to poor image quality
How to Avoid Mistakes
- Ensure adequate injected dose and acquisition time for sufficient count statistics
- Use resolution recovery (distance-dependent PSF modeling) in iterative reconstruction
- Apply CT-based attenuation correction; verify CT-SPECT registration
- Use motion detection and correction algorithms; shorter acquisitions with CZT cameras
- Verify energy window settings match the radionuclide photopeak and scatter windows
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred (64,64) image, but SPECT acquires projections of shape (n_angles, n_detectors) using a rotating gamma camera with collimator — output shape (32,64) vs (64,64)
- SPECT measurement involves collimated gamma-ray detection with depth-dependent spatial resolution (the collimator PSF broadens with distance) — the widefield spatially-invariant Gaussian blur cannot model this depth-dependent response
How to Correct the Mismatch
- Use the SPECT operator that models collimated gamma-ray projection with distance-dependent resolution: y(theta,s) = integral of (h(d) * f) along projection rays for each angle
- Reconstruct using OSEM with depth-dependent collimator-detector response modeling and attenuation correction (Chang method or CT-based mu-map)
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Hudson & Larkin, 'Accelerated image reconstruction using ordered subsets of projection data (OSEM)', IEEE TMI 13, 601-609 (1994)
Canonical Datasets
- Clinical SPECT benchmark collections
SPECT/CT
SPECT/CT
Spectral CT
Spectral CT
Susceptibility-Weighted Imaging (SWI)
Susceptibility-Weighted Imaging (SWI)
Ultrasound Imaging
Ultrasound imaging forms images by transmitting acoustic pulses into tissue and recording echoes reflected from impedance boundaries. In ultrafast plane-wave imaging, unfocused plane waves at multiple steering angles are transmitted and the received channel data are coherently compounded using delay-and-sum (DAS) beamforming. The forward model is governed by the acoustic wave equation with tissue-dependent speed of sound and attenuation. Primary degradations include speckle noise (coherent interference), limited bandwidth, and aberration from heterogeneous tissue.
Ultrasound Imaging
Description
Ultrasound imaging forms images by transmitting acoustic pulses into tissue and recording echoes reflected from impedance boundaries. In ultrafast plane-wave imaging, unfocused plane waves at multiple steering angles are transmitted and the received channel data are coherently compounded using delay-and-sum (DAS) beamforming. The forward model is governed by the acoustic wave equation with tissue-dependent speed of sound and attenuation. Primary degradations include speckle noise (coherent interference), limited bandwidth, and aberration from heterogeneous tissue.
Principle
Medical ultrasound imaging transmits short pulses of high-frequency sound waves (1-20 MHz) into tissue and detects the echoes reflected from acoustic impedance boundaries. The time delay of each echo determines the reflector depth, and beamforming focuses the transmitted and received beams to form a 2-D cross-sectional image. Spatial resolution improves with frequency but penetration depth decreases.
How to Build the System
A clinical ultrasound system consists of a multi-element transducer array (linear 7-15 MHz for superficial, curvilinear 2-5 MHz for abdominal, phased array 1-5 MHz for cardiac) connected to a beamformer and image processor. Modern systems use 128-192 element arrays with digital beamforming. Apply acoustic coupling gel between transducer and skin. Adjust gain, depth, focus, and frequency for the specific examination.
Common Reconstruction Algorithms
- Delay-and-sum (DAS) beamforming
- Adaptive beamforming (Capon, MVDR) for improved resolution
- Synthetic aperture focusing (SAFT)
- Plane-wave compounding for ultrafast imaging
- Deep-learning beamforming and speckle reduction
Common Mistakes
- Incorrect transducer selection (frequency too high for deep structures or too low for superficial)
- Poor acoustic coupling (air gaps) causing signal dropout
- Gain set too high, saturating the image and masking pathology
- Acoustic shadowing behind highly reflective structures misinterpreted as pathology
- Not adjusting focus zone depth to the region of interest
How to Avoid Mistakes
- Select transducer frequency appropriate for the imaging depth required
- Apply generous coupling gel and maintain constant contact pressure
- Adjust TGC (time-gain compensation) curve for uniform brightness with depth
- Recognize and account for acoustic artifacts (shadowing, enhancement, reverberation)
- Set the transmit focal zone at the depth of the target structure
Forward-Model Mismatch Cases
- The widefield fallback produces a 2D (64,64) image, but ultrasound acquires RF channel data of shape (n_depths, n_channels) from each transducer element — output shape (32,128) vs (64,64) makes beamforming algorithms incompatible
- Ultrasound imaging involves wave propagation, reflection at tissue interfaces, and time-of-flight encoding — the widefield Gaussian blur has no relationship to acoustic wave physics (speed of sound, impedance mismatch, attenuation)
How to Correct the Mismatch
- Use the ultrasound operator that models acoustic pulse transmission, tissue reflection, and per-element receive: each channel records the time-domain echo signal from scatterers at different depths
- Reconstruct B-mode images using delay-and-sum beamforming or adaptive beamforming (MVDR, coherence factor) that require the correct RF channel data format and speed-of-sound model
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Montaldo et al., 'Coherent plane-wave compounding for very high frame rate ultrasonography', IEEE TUFFC 56, 489-506 (2009)
- Liebgott et al., 'PICMUS: Plane-wave Imaging Challenge in Medical Ultrasound', IEEE IUS 2016
Canonical Datasets
- PICMUS Challenge (plane-wave ultrasound)
- CUBDL (deep learning ultrasound beamforming)
X-ray Angiography
Digital subtraction angiography (DSA) visualizes blood vessels by subtracting a pre-contrast mask image from post-contrast images acquired after injecting iodinated contrast agent. The subtraction eliminates static anatomy, isolating vascular structures. The forward model is y_post - y_pre = Delta_mu * t_vessel + n where Delta_mu is the attenuation increase from iodine. Primary challenges include patient motion between mask and contrast frames, breathing artifacts, and superposition of overlapping vessels.
X-ray Angiography
Description
Digital subtraction angiography (DSA) visualizes blood vessels by subtracting a pre-contrast mask image from post-contrast images acquired after injecting iodinated contrast agent. The subtraction eliminates static anatomy, isolating vascular structures. The forward model is y_post - y_pre = Delta_mu * t_vessel + n where Delta_mu is the attenuation increase from iodine. Primary challenges include patient motion between mask and contrast frames, breathing artifacts, and superposition of overlapping vessels.
Principle
X-ray angiography visualizes blood vessels by injecting iodinated contrast agent and acquiring rapid-sequence fluoroscopic images. Digital Subtraction Angiography (DSA) subtracts a pre-contrast mask image from post-contrast frames, removing bone and soft tissue to show only the contrast-filled vasculature with high contrast and spatial resolution.
How to Build the System
Use a biplane or single-plane angiography suite with high-speed flat-panel detectors (30-60 fps capability). The C-arm provides multi-angle positioning. Power injector delivers iodinated contrast (350-370 mgI/mL) at controlled rates. Road-mapping mode overlays vessel map on live fluoro for catheter guidance. 3-D rotational angiography acquires a spin to reconstruct a volume of the vasculature.
Common Reconstruction Algorithms
- Digital subtraction (mask-live image subtraction)
- Pixel shifting for motion compensation in DSA
- 3-D rotational angiography reconstruction (FDK or iterative)
- Time-density curve analysis for perfusion assessment
- Deep-learning vessel segmentation and stenosis quantification
Common Mistakes
- Patient motion between mask and contrast frames causing misregistration artifacts
- Inadequate contrast bolus timing causing suboptimal vessel opacification
- Overexposure or underexposure of the detector outside the linear range
- Bowel gas or cardiac motion causing subtraction artifacts
- Injecting contrast too fast, creating reflux or missing distal vessels
How to Avoid Mistakes
- Instruct patients to remain still; use pixel shifting or elastic registration
- Use test bolus or timing run to determine optimal injection-to-imaging delay
- Use automatic dose rate control; verify detector within calibrated dynamic range
- Use cardiac gating for coronary or thoracic angiography
- Adjust injection rate and volume to vessel size and flow characteristics
Forward-Model Mismatch Cases
- The widefield fallback applies Gaussian blur, but angiography uses X-ray transmission with iodine contrast agent — the exponential attenuation model with contrast-enhanced vessels is not a simple convolution
- Digital subtraction angiography (DSA) requires temporal subtraction between pre- and post-contrast images to isolate vessels — the widefield model has no temporal component and cannot model contrast dynamics
How to Correct the Mismatch
- Use the angiography operator implementing contrast-enhanced X-ray transmission: y = I_0 * exp(-(mu_tissue*t + mu_iodine*c(t))) where c(t) models contrast agent concentration dynamics
- Apply temporal subtraction (post-contrast minus pre-contrast) or parametric mapping of contrast kinetics using the correct time-resolved forward model
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Defined by clinical DSA standards (ACC/AHA guidelines)
Canonical Datasets
- IntrA (intracranial aneurysm 3DRA dataset)
X-ray Computed Tomography
X-ray CT reconstructs cross-sectional images from a set of line-integral projections (sinogram) acquired as an X-ray source and detector array rotate around the patient. The forward model is the Radon transform: y = R*x + n where R computes line integrals along each ray. Sparse-view and low-dose protocols reduce radiation but introduce streak artifacts and noise. Reconstruction uses filtered back-projection (FBP) or iterative methods (MBIR, DL post-processing).
X-ray Computed Tomography
Description
X-ray CT reconstructs cross-sectional images from a set of line-integral projections (sinogram) acquired as an X-ray source and detector array rotate around the patient. The forward model is the Radon transform: y = R*x + n where R computes line integrals along each ray. Sparse-view and low-dose protocols reduce radiation but introduce streak artifacts and noise. Reconstruction uses filtered back-projection (FBP) or iterative methods (MBIR, DL post-processing).
Principle
X-ray Computed Tomography reconstructs cross-sectional images from multiple X-ray projection measurements acquired at different angles around the patient. The Beer-Lambert law governs X-ray attenuation: I = I₀ exp(-∫μ(x,y) dl), and the Radon transform relates projections to the attenuation map. Filtered back-projection or iterative algorithms invert the Radon transform to produce volumetric images.
How to Build the System
A clinical CT scanner consists of a rotating gantry with an X-ray tube (80-140 kVp, 50-800 mA) and a curved detector array (64-320 rows of scintillator-photodiode elements) on opposing sides. The gantry rotates at 0.25-0.5 s per revolution. Helical scanning moves the patient table continuously through the gantry. Key calibrations: air scans, detector gain normalization, beam-hardening correction LUTs, and geometric calibration.
Common Reconstruction Algorithms
- Filtered back-projection (FBP) with Ram-Lak or Shepp-Logan filter
- FDK (Feldkamp-Davis-Kress) for cone-beam geometry
- Iterative reconstruction: SART, OS-SIRT
- Model-based iterative reconstruction (MBIR) with statistical noise model
- Deep-learning reconstruction (FBPConvNet, LEARN, WGAN-VGG for low-dose CT)
Common Mistakes
- Ring artifacts from uncorrected detector gain variations
- Beam-hardening artifacts (cupping, streaks near bone/metal) not corrected
- Patient motion during scan causing blurring and streaks
- Insufficient angular sampling producing streak or aliasing artifacts
- Metal artifacts from implants overwhelming reconstruction algorithms
How to Avoid Mistakes
- Perform regular air calibrations and detector flatfield corrections
- Apply polynomial beam-hardening correction or dual-energy decomposition
- Use gating (cardiac/respiratory) or fast rotation to reduce motion artifacts
- Ensure adequate number of projections (≥ π × detector columns for FBP)
- Use metal artifact reduction algorithms (MAR, iterative forward-projection inpainting)
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred (64,64) image, but CT acquires a sinogram of shape (180,64) via the Radon transform (line integrals at multiple angles) — any reconstruction algorithm expecting sinogram input will crash
- The Gaussian blur preserves spatial structure, but the Radon transform converts spatial information into angular projections — the fallback output bears no physical relationship to X-ray transmission measurements
How to Correct the Mismatch
- Use the CT operator implementing the discrete Radon transform: y(theta,s) = integral of f(x,y) along line at angle theta and offset s, producing a (n_angles, n_detectors) sinogram
- Reconstruct using filtered back-projection (FBP) or iterative algorithms (SART, ADMM-TV) that require the correct Radon transform / back-projection pair
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Feldkamp et al., 'Practical cone-beam algorithm', J. Opt. Soc. Am. A 1, 612-619 (1984)
- Leuschner et al., 'LoDoPaB-CT, a benchmark dataset for low-dose CT reconstruction', Scientific Data 8, 109 (2021)
Canonical Datasets
- LoDoPaB-CT (Scientific Data 2021)
- DeepLesion (NIH Clinical Center)
- AAPM Low-Dose CT Grand Challenge
X-ray Radiography
Digital X-ray radiography produces a 2D projection image by transmitting X-rays through the body onto a flat-panel detector. The forward model follows Beer-Lambert attenuation: y = I_0 * exp(-integral(mu(s) ds)) + n where mu is the linear attenuation coefficient along each ray. The image is a superposition of all structures along the beam path. Primary degradations include quantum noise (Poisson), scatter, and geometric magnification artifacts.
X-ray Radiography
Description
Digital X-ray radiography produces a 2D projection image by transmitting X-rays through the body onto a flat-panel detector. The forward model follows Beer-Lambert attenuation: y = I_0 * exp(-integral(mu(s) ds)) + n where mu is the linear attenuation coefficient along each ray. The image is a superposition of all structures along the beam path. Primary degradations include quantum noise (Poisson), scatter, and geometric magnification artifacts.
Principle
X-ray radiography produces a 2-D projection image of the patient's internal structures by measuring the transmitted X-ray intensity after passing through the body. Dense structures (bone, metal) attenuate more X-rays and appear bright on the detector. The image represents the line-integral of the attenuation coefficient along each ray path.
How to Build the System
An X-ray tube (stationary or rotating anode, 40-150 kVp) produces a divergent beam. The patient stands or lies between the tube and a flat-panel detector (amorphous silicon with CsI scintillator, or amorphous selenium for direct conversion). Anti-scatter grid (Bucky grid) is placed before the detector. Automatic exposure control (AEC) sets mAs based on patient thickness. Calibration includes dark field, flatfield, and defective pixel mapping.
Common Reconstruction Algorithms
- Flat-field correction (gain/offset normalization)
- Logarithmic transform for linear attenuation mapping
- Anti-scatter grid artifact removal
- Dual-energy subtraction (bone/soft-tissue separation)
- Deep-learning denoising for low-dose radiography
Common Mistakes
- Under-exposure causing excessive quantum noise, especially in obese patients
- Grid artifacts from misaligned anti-scatter grid
- Patient motion blur in long-exposure radiographs
- Incorrect windowing (display LUT) obscuring diagnostic information
- Scatter radiation degrading image contrast in thick body parts
How to Avoid Mistakes
- Use AEC and verify exposure indicator falls within acceptable range
- Ensure grid is properly aligned with the X-ray focal spot distance
- Use shortest possible exposure time; instruct patient to hold breath
- Apply appropriate DICOM windowing presets for the anatomical region
- Use an appropriate anti-scatter grid ratio (8:1 to 12:1) for thick body parts
Forward-Model Mismatch Cases
- The widefield fallback applies additive Gaussian blur, but X-ray radiography follows Beer-Lambert attenuation: I = I_0 * exp(-integral(mu(x,y,z) dz)) — the exponential transmission model is fundamentally different from linear convolution
- The Gaussian blur preserves mean intensity, but X-ray attenuation reduces intensity exponentially with material thickness and density — the fallback cannot model absorption contrast, bone/soft-tissue differentiation, or scatter
How to Correct the Mismatch
- Use the X-ray radiography operator implementing Beer-Lambert transmission: y = I_0 * exp(-A*x) + scatter + noise, where A is the projection matrix along the beam direction
- Include scatter rejection (anti-scatter grid model), detector response (DQE), and quantum noise (Poisson statistics) for physically accurate forward modeling
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Irvin et al., 'CheXpert: A large chest radiograph dataset', AAAI 2019
- Wang et al., 'ChestX-ray8: Hospital-scale chest X-ray database', CVPR 2017
Canonical Datasets
- CheXpert (Stanford, 224K studies)
- MIMIC-CXR (MIT/BIDMC, 377K images)
- NIH ChestX-ray14 (112K images)